Problem # p010

2-D motion of solid body
A billiard ball is hit in an oblique fashion by the cue and experiences a force P as shown in the figure (top view). Consider the force P, the angle β, the mass m, the radius r, and the polar mass moment of inertia = 2/5 m r² of the billiard ball as given.
  1. Write out the equations for the x- and y-component of the acceleration of the center of mass due to force P.

  2. Write out the equation for the angular acceleration of the ball due to force P.

  3. Use the results from (1) and (2) and the concept of relative acceleration to derive the equation for the acceleration of point 1, the point at which P is hitting the ball assuming that at the the angular velocity of the ball is still zero.